Unpolarised light is passed through two ideal polarisers as shown in the figure. The axis of polarisation of the first polariser that the light passes through is horizontal. The axis of polarisation of the second polariser is vertical. Which of the following correctly describes how the light would emerge from the second polariser?
In the figure, we see unpolarised light represented by the arrow passing through two polarisers. The first polariser has an axis of polarisation that is horizontal, as represented by the horizontal lines in the figure. The second polariser has an axis of polarisation that is vertical, as represented by the vertical lines in the figure.
Light is an electromagnetic wave, which means that it has fluctuating electric and magnetic fields which are perpendicular to each other. The light is initially described as unpolarised, which means that the orientation of the electric and magnetic fields are equally distributed circularly.
Next to the figure, we can draw in the initial light as represented by the unpolarised electric fields. It is common convention to use the polarisation of electric fields when dealing with polarising light. The first polariser is horizontally oriented. This means that the polariser will only allow the electric fields that are vibrating horizontally to pass through. Think of a picket fence turned on its side. And that only the light that is vibrating parallel to the slots in the fence will be able to make it through. Everything else will be blocked.
When unpolarised light passes through a polariser, the intensity of the transmitted light is one-half of what it is coming in. The horizontally polarised light now tries to pass through the vertically oriented polariser. Once again, think about a picket fence with slots between the boards. The only light that’ll be able to pass through will have electric fields vibrating parallel to the slots, in this case vertically.
Because all the light that passes through the first polariser has horizontally vibrating electric fields. There is no component of the light that’s left that has vertically vibrating electric fields. Therefore, there is no light that will pass through the second polariser after having passed through the first.
Looking at our possible answers, we can see that choice b) — no light would emerge from the second polariser — would match what we just found. It’s always a good idea to look at the other answers to make sure that we have confidence in the one that we chose.
In order for the light to be polarised at 45 degrees to the vertical as choice a) suggests, I would have to have a 45-degree-oriented polariser. Since the problem and the figure do not show a 45-degree-oriented polariser, we know that this cannot be true. If choice c) was correct and the light continued to be unpolarised, then our light would not pass through any polarisers at all.
If the question asks us for the orientation of the light after the first polariser, then choice d) could be correct. After the light passes through the first polariser, it is horizontally polarised. However, since the second polariser is vertically oriented, none of the horizontally polarised light can get through.
For answer choice e) to be correct, we would have to have skipped the first polariser. If the unpolarised light only went through the vertically oriented polariser, then the emerging light would also be vertically polarised.
Not only can we show that choice b) is correct conceptually, we can also show that all the other choices are not correct. This gives us extra confidence in our answer.